Let $B= A^*A$ where $A$ is a normal linear operator on a hilbert space $X$.
Then how can I show that $||{B^2}^n||^{\frac{1}{2^n}} = ||B||?$
I tried using induction but am not able to get anything.
Further using this, how can I show that $||{A^2}^n|| = {||A||^2}^n$?
For the latter, Since $A$ is normal, I have derived that $||{A^2}^n||^2 = {||A||^2}^{n+1}$